Does the delta-epsilon limit definition in reverse work for describing limits in monotonic functions?
By reversed, one means for
lim (x -> a) f(x) = L
if for each δ there corresponds ε such that
0 < | x-a | < δ whenever | f(x) - L | < ε.
The Attempt at a Solution
I am thinking that it works, because this definition means that the range interval must lie within the domain interval, and it can be seen that shrinking δ also shrinks ε, which is how the usual definition works but in reverse.
I don't think this would work for non-monotonic functions because there can be many f(x) that satisfy
| f(x) - L | < ε but not | f(x) - L | < ε. Hopefully someone can also confirm this part too.